The Ligue 1 side submitted an offer for left-footed centre-back Lucumi, 22, earlier in the week.
However, they will need to improve their proposal with Genk snubbing a bid of ‘just over’ €10m.
Genk want to keep Lucumi, who signed from Deportivo Cali in 2018, for at least another year.
Lucumi made 22 appearances in Jupiler Pro League this season and a further six in the UEFA Champions League for Genk.
Rennes want one or two new defenders after losing Joris Gnagnon (returning to Sevilla after a loan) and Jeremy Morel (end of contract).